Railway Coupled Ballasted Track-Bridge System: Mode Shape Sensitivities For Damage Detection

In this study, a theoretical investigation is conducted to analyze how the sensitivity of modal characteristics (mode shapes) in a coupled track-bridge system to structural damage influences the behavior of railway structure. The system under study comprises two straight, parallel, uniform Bernoulli-Euler (B-E) beams, interconnected by uniform vertical springs that model the vertical interaction between the ballasted track and the bridge deck (TBI). For that, a Finite Element model (FE) is implemented, and two methods – Nelson’s method and Modal method – are presented for calculating the mode shape sensitivities (derivatives) to enable comparative analysis. Additionally, the Finite Difference Method (FDM) is employed to approximate the curvature of the eigenvector sensitivity, aiming to assess the feasibility of localizing potential damage in both the rail and bridge deck. Results highlight the significance of lower-order mode sensitivity for single damaged-scenarios. However, in cases of multiple damages, challenges arise in identifying precisely the defect locations. Conversely, the curvature of mode-shape sensitivity proves efficiency for damage localization in the coupled system, even when single or multiple damaged elements are present.